Spatial dispersion and optics of crystals

Abstract

Many liquid crystal compounds are known to give structures periodic in only one direction, say z, with a period p comparable with the light wavelength . Their optical properties are fully defined by a dielectric tensor field (z), which for most crystals is well known. For p<, the periodic structures behave optically as homogeneous, and can be effectively described by a constant dielectric tensor explicitly depending on the ratio (p/). A very general method to relate (p/) to (z) is presented, based on the transfer matrix for a thin layer of the periodic medium between planes perpendicular to z. Fully analytic and very simple equations are presented, and used to find the conditions where a description of the periodic medium in terms of a constant dielectric tensor is allowed, and more generally to discuss the limits of validity of homogeneous models for crystals.